In the mining industry, once material of value, such as ore situated below the surface of the ground, has been discovered, there exists a need to extract that material from the ground.
In the past, one more traditional method has been to use a relatively large open cut mining technique, whereby a great volume of waste material is removed from the mine site in order for the miners to reach the material considered of value. For example, referring to FIG. 1, the mine 101 is shown with its valuable material 102 situated at a distance below the ground surface 103. In the past, most of the (waste) material 104 had to be removed so that the valuable material 102 could be exposed and extracted from the mine 101. In the past, this waste material was removed in a series of progressive layers 105, which are ever diminishing in area, until the valuable material 102 was exposed for extraction. This is not considered to be an efficient mining process, as a great deal of waste material must be removed, stored and returned at a later time to the mine site 101, in order to extract the valuable material 102. It is desirable to reduce the volume of waste material that must be removed prior to extracting the valuable material.
The open cut method exemplified in FIG. 1 is viewed as particularly inefficient where the valuable resource is located to one side of the pit 105 of a desirable mine site 101. For example, FIG. 2 illustrates such a situation. The valuable material 102 is located to one side of the pit 105. In such a situation, it is not considered efficient to remove the waste material 104 from region 206, that is where the waste material is not located relatively close to the valuable material 102, but it is considered desirable to remove the waste material 104 from region 207, that is where it is located nearer to the valuable material 102. This then brings other considerations to the fore. For example, it would be desirable to determine the boundary between regions 206 and 207, so that not too much undesirable waste material is removed (region 206), yet enough is removed to ensure safety factors are considered, such as cave-ins, etc. This then leads to a further consideration of the need to design a ‘pit’ 105 with a relatively optimal design having consideration for the location of the valuable material, relative to the waste material and other issues, such as safety factors.
This further consideration has led to an analysis of pit design, and a technique of removing waste material and valuable material called ‘pushbacks’. This technique is illustrated in FIG. 3. Basically, the pit 105 is designed to an extent that the waste material 104 to be removed is minimised, but still enabling extraction of the valuable material 102. The technique uses ‘blocks’ 308 which represent smaller volumes of material. The area proximate the valuable material is divided into a number of blocks 308. It is then a matter of determining which blocks need to be removed in order to enable access to the valuable material 102. This determination of ‘blocks 308’, then gives rise to the design or extent of the pit 105.
FIG. 3 represents the mine as a two dimensional area, however, it should be appreciated that the mine is a three dimensional area. Thus the blocks 308 to be removed are determined in phases, and cones, which represent more accurately a three dimensional ‘volume’ which volume will ultimately form the pit 105.
Further consideration can be given to the prior art situation illustrated in FIG. 3. Consideration should be given to the scheduling of the removal of blocks. In effect, what is the best order of block removal, when other business aspects such as time/value and discounted cash flows are taken into account? There is a need to find a relatively optimal order of block removal which gives a relatively maximum value for a relatively minimum effort/time.
Attempts have been made in the past to find this ‘optimum’ block order by determining which block(s) 308 should be removed relative to a ‘violation free’ order. Tuning to the illustration in FIG. 4, a pit 105 is shown with valuable material 102. For the purposes of discussion, if it was desirable to remove block 414, then there is considered to be a ‘violation’ if we determined a schedule of block removal which started by removing block 414 or blocks 414, 412 & 413 before blocks 409, 410 and 411 were removed. In other words, a violation free schedule would seek to remove other blocks 409, 410, 411, 412 and 413 before block 414. (It is important to note that the block number does not necessarily indicate a preferential order of block removal).
It can also be seen that this block scheduling can be extended to the entire pit 105 in order to remove the waste material 104 and the valuable material 102. With this violation free order schedule in mind, prior art attempts have been made. FIG. 5 illustrates one such attempt. Taking the blocks of FIG. 4, the blocks are numbered and sorted according to a ‘mineable block order’ having regard to practical mining techniques and other mine factors, such as safety etc and is illustrated by table 615. The blocks in table 515 are then sorted 516 with regard to Net Present Value (NPV) and is based on push back design via Life-of-mine NPV sequencing, taking into account obtaining the most value block from the ground at the earliest time. To illustrate the NPV sorting, and turning again to FIG. 4, there is a question as which of blocks 409, 410 or 411 should be removed first. All three blocks can be removed from the point of view of the ability to mine them, but it may, for example, be more economic to remove block 410, before block 409. Removing blocks 409, 410 or 411 does not lead to ‘violations’ thus consideration can be given to the order of block removal which is more economic.
NPV sorting is conducted in a manner which does not lead to violations of the ‘violation free order’, and provides a table 517 listing an ‘executable block order’. In other words, this prior art technique leads to a listing of blocks, in an order which determines their removal having regard to the ability to mine them, and the economic return for doing so.
Nonetheless, the foregoing description and prior art techniques, are considered to ignore a number of key problems encountered in a typical mine implementation. An ore body in the ground is typically modeled as a three-dimensional grid of blocks. Each of these blocks has attributes, such as the tonnage of rock and ore contained in the block. Given a three-dimensional block model of an ore body, the mine planner determines an extraction schedule (an extraction ordering of the blocks). In practice, an extraction must satisfy a number of constraints. For example, wall slopes must be maintained below a defined value to avoid pit walls collapsing and the rates of both removal of earth from the pit (mining rate) and ore processing (processing rate) must not exceed given limits. The wall slope constraints are usually taken into account using precedence relations between blocks. The removal of a given block requires the earlier removal of several blocks above it; that is removal of these several blocks must precede removal of the given block.
Typically, the blocks of highest value lie near the bottom of the ore body, far underneath the ground. A cash flow stream is generated when these blocks are excavated and the ore within them is sold. Because one can earn interest on cash received earlier, the value of a block increases if it is excavated earlier, and decreases (or is discounted) if it is excavated later. This concept of discounting is central to the notion of net present value (NPV). Thus the mine planner seeks an extraction schedule that maximizes the net present value of the ore body. The, net present value forms the objective function of this optimization problem.
Calculating the NPV of an extraction schedule is far from easy. In current approaches, each block is simply ascribed a value in dollars, but in many cases, this value may be only a very crude approximation, and subject to change. For commodities such as copper, the planner needs to know Fe metal content of the block, the selling price at all future times within the planning horizon, the mining/processing costs, and some other factors. This is a difficult and problematic in itself.
However, for blended products such as coal or iron ore, the problem is considered even more difficult. This follows from the fact that the values of individual blocks are not known until those blocks have been blended with other blocks to form a saleable product. An individual block may be of sufficiently low quality to be considered worthless or waste material in isolation. A block having a relatively average quality may attract a certain price, given the price set for the material is based on a minimum quality level. Thus when a block having a relatively higher quality is extracted, this block will receive only the same value as the average quality block because the value is based on a minimum quality level. For this reason, the low quality block, when blended with the high quality block result in a volume of ore at or above the minimum quality level and thus the two ore blocks may be both sold. This ‘blended’ price is significantly more than the low quality and high quality blocks would be worth in isolation. This enables more revenues to be achieved from the extraction of resource(s). Blending is also particularly valuable for smoothing the grade of ore blocks sold when the grade of ore blocks coming out of the pit is relatively erratic. Thus, the value of a block is unknown until it is part of a blended extraction schedule.
In addition to the factors described above, the sheer dimensions of the problem confronting a mine planner, with hundreds of thousands of blocks and up to a 30-year time horizon make it very difficult to find an extraction schedule that maximizes the total NPV of the mine very difficult.
It is considered that some prior art approaches approximate heavily, by aggregating either blocks or time periods, are considered to solve the problem in a piecemeal fashion, or relying on heuristic methods. The treatment of blending is considered to be done by relatively crude approximations. The prior art assumes a value and then seeks to optimise a schedule. But if the assumed value is not correct, especially over a relatively long period of time, then the schedule could not be considered optimal.
Other prior art approaches, in the form of some commercial software, enable post-schedule blend optimization to be performed. The software determines an extraction schedule based on estimated “in pit” valuation of each block, and then a blending schedule is developed based on the extraction sequence given. This is considered not very accurate in a commercial situation as the in-pit valuations are estimates, and thus may be far from reflecting a true resulting blended value. Furthermore, the blending schedule itself is often determined by heuristic methods, which may yield far from optimal solutions.
The Whittle Four-X Analyser (by Whittle Pty Ltd) attempts to integrate scheduling and blending by iteratively updating the schedule and blend using a hill-climbing heuristic, although the blending optimization is still local in time. MineMAX (by MineMax Pty Ltd) and ECSI Minex Maximiser (by ECS International Pty Ltd) have partially integrated scheduling and blending. However, the blocks are valued “in ground” in isolation, riot as part of a blend, and the blending optimization is performed locally in time due to problem size limitations.
Given the importance of blending, it is essential to consider these factors as an integral part of schedule development improvements in the accuracy of the mine model and analysis techniques will dearly lead to increased mine value which can lead to increased revenues in the order of many millions of dollars over the life of a relatively large mine.
With regard to prior art techniques, in as much as the removal of material is concerned, is based substantially on the assumption that the data gathered from sample drillings is an accurate reflection of the homogeneity of the entire mine pit. Unfortunately, in many cases of the prior art, what has been revealed underneath the ground over the life of the mine, has differed from what was ‘expected’ to be found based on the sample drillings and geological survey data initially obtained. The difference may manifest itself in grade of material or waste.
Although the difference may be marginal from one block to another, or with regard to a slight variation in grade or quality of ore, when taken globally over a mine project both in magnitude and time, the difference can represent many millions of dollars between what actually was mined, and what was expected when the mine was designed.
One reason for this is that the design of prior art mines is based substantially entirely on this sample, geological survey data. Thus if the data is wrong, or inaccurate, then the design established for the mine will not be found to be optimal for that particular mine location. Again, unfortunately, this will usually only be realised well after the design has been established and implemented. By this time it is, or it may be considered, too late to correct or alter the mine design. The result will be this (wasteful) expenditure of possibly many millions of dollars in creating a mine according to a design that was not ‘optimal’.
In considering the problem posed, it will be helpful to gain a better understanding of prior art mine ‘design’ techniques. In general, a geographical survey establishes data used as the basis of a mine design. The ‘design’ is necessary to provide determination of the various commercial aspects associated with a mine, and for establishing a block ‘schedule’; that is an executable order of blocks from the mine.
This survey data manifests itself in, for example, 10 or 20 different samples and analyses of the potential mine location and site. A number of simulations and interpolations are made based on the data in order to predict a mine plan, which can be considered an order for taking material (ore and/or waste) from the location of the potential mine. It is then necessary to establish ‘the’ (one) mine plan which is to be implemented.
Typically, the blocks of highest value lie near the bottom of the ore body, far underneath the ground. A cash flow stream is generated when these blocks are excavated and the ore within them is sold. Because one can earn interest on cash received earlier, the value of a block increases if it is excavated earlier, and decreases (or is discounted) if it is excavated later. This concept of discounting is central to the notion of net present value (NPV). Thus the mine planner seeks an extraction schedule that maximizes the net present value of the ore body. The net present value forms the objective function of this optimization problem.
As previously mentioned, calculating the NPV of an extraction schedule is far from easy. In current approaches, each block is simply ascribed a value in dollars, but in many cases, this value may be only a very crude approximation, and subject to change. For commodities such as copper, the planner needs to know the metal content of the block, the selling price at all future times within the planning horizon, the mining/processing costs, and some other factors. This is a difficult and problematic in itself.
In some cases, a random selection may have been made from the simulations and interpolations. An example of this is “AN APPLICATION OF BRANCH AND CUT TO OPEN PIT MINE SCHEDULING” by Louis Caccetta and Stephen P. Hill. A copy may be found at website: http://rutcor.rutgers.edu/˜do99/EA/SHijl.doc.
In other instances, an ‘average’ of the various simulations is taken and which assumes a fixed pricing in the interpolation(s) calculated, where the ‘average’ has been taken as ‘the’ mine design.
Furthermore, a number of prior art techniques are considered to take a relatively simple view of the problems confronted by the mine designer in a ‘real world’ mine situation. For example, the size, complexity, nature of blocks, grade and other engineering constraints and time taken to undertake a mining operation is often not fully taken into account in prior art techniques, leading to computational problems or errors in the mine design. Such errors can have significant financial and safety implications for the mine operator.
With regard to size, for example, prior art techniques fall to adequately take account of the size of a ‘block’. Depending on the size of the overall project, a ‘block’ may be quite large, taking some weeks, months or even years to mine. If this is the case, many assumptions made in prior art techniques fail to give sufficient accuracy for the modern day business environment.
Given that many of the mine designs are mathematically and computational complex, according to prior art techniques, if the size of the blocks were reduced for greater accuracy, the result will be that either the optimisation techniques used will be time in feasible ( that is they will take an inordinately long time to complete), or other assumptions will have to be made concerning aspects of the mine design such as mining rates, processing rates, etc which will result in a decrease the accuracy of the mine design solution.
Some examples of commercial software do use mixed integer programming engines, however, the method of aggregating blocks requires further improvement. For example, it is considered that product ‘ECSI Maximiser’ by ECS international Pty Ltd uses a form of integer optimisation in their pushback design, but the optimisation is local in time, and it's problem formulation is considered too large to optimise globally over the life of a mine. Also the product ‘MineMax’ by MineMAX Ptd Ltd may be used to find a rudimentary optimal block sequencing with a mixed integer programming engine, however it is considered that its method of aggregation does not respect slopes as is required in many situations. ‘MineMax’ also optimises locally in time, and not globally. Thus, where there is a large number of variables, the user must resort to subdividing the pit into separate sections, and perform separate optimisations on each section, and thus the optimisation is not global over the entire pit it is considered desirable to have an optimisation that is global in both space and time.
There still exists a need, however, to improve prior art techniques. Given that mining projects, on the whole, are relatively large scale operations, even small improvements in prior art techniques can represent millions of dollars in savings, and/or greater productivity and/or safety. There is a need to improve mine design and/or the method(s) used to design a mine.
An object of the present invention is to provide an improved method of determining a cluster.
Another object of the present invention is to alleviate at least one disadvantage of the prior art.
Another object of the present invention is to provide an improved method of block removal, and/or an improved pit design and/or executable block order.
Any discussion of documents, devices, acts or knowledge in this specification is included to explain the context of the invention. It should not be taken as an admission that any of the material forms a part of the prior art base or the common general knowledge in the relevant art in Australia or elsewhere on or before the priority date of the disclosure and claims herein.